Throughout the manuscript, \(\mathbb {F}_{q}\)  is the field with \(q\)  elements; however, in this, we work over \(\mathbb {F}_{2^3}\)  and more generally \(\mathbb {F}_{2^n}\)  for \(n\in \mathbb {N}\) . Given a code \(C\)  over \(\mathbb {F}_{q^n}\) , the code \(C^{(q)}\)  over \(\mathbb {F}_{q}\)  is constructed using the trace map in [1]}. The code \(C^{(q)}\)  is referred to as subfield code with respect to \(C\) . Hyun et al. [2]} studied linear codes by choosing some specific defining set obtained using simplicial complexes and produced certain families of binary optimal linear codes. In [3]}, Hyun et al. used posets in place of simplicial complexes to study linear codes. They constructed binary linear codes that are minimal as well as optimal, but the Ashikhmin-Barg condition [4]} does not hold for them. In 2021, Zhu et al. studied codes over \(\mathbb {F}_{4}\)  and produced minimal optimal codes. In [5]}, the authors studied linear codes over \(\mathbb {F}_{4}\)  and the corresponding subfield codes, and obtained their weight distributions. They used simplicial complexes to construct defining set and produced two infinite families of optimal linear codes. The weight distribution of a linear code is an important research topic in coding theory because it can be used to calculate the error correcting capability as well as the error probability of error detection and correction [6]}, [7]}, [8]}. The minimum Hamming distance of linear codes are well known for their importance in determining error-correcting capacity. As a result, finding optimal linear codes has become one of the central topics for researchers. A lot of work has been done in the recent past. In [2]}, Hyun et al. shows how optimal codes can be utilized for the construction of secret sharing schemes having nice access structures following the framework discussed in [10]}. The secret sharing schemes are essential nowadays; in fact, these are used heavily in electronic voting systems, cryptographic protocols, banking systems etc. Minimal codes are helpful to construct the access structure of the secret sharing schemes [6]}, [12]}.
